A method is presented for hand calculation of the one-sided inverse of the transfer function matrix for time invariant linear systems. Unlike conventional methods, this procedure does not require the inversion of the matrix (sI - A). For single input single output systems, the procedure leads to a direct calculation of the transfer function. In the third part of this paper, we show how to use block matrix operations to reduce the dimensions of the matrices involved in the method. An example is given to illustrate the method.